The newer HTML5 structuring elements appear in Internet Explorer 9 and above and in all other major modern browsers. Discussion around some of these elements is still ongoing as I write this. Some browsers are beginning to support a main element despite opposition from spec editor Ian Hickson, whereas other elements such as hgroup are at risk of being dropped.
Using the attribute-based accessibility and semantic extensions WAI-ARIA, microformats, RDFa, and microdata in any browser is completely safe. The microdata API is implemented in Firefox and Opera.
Data attributes are also supported in all browsers, although the API using dataset is not present in Internet Explorer or Android 2.3 and below. The jQuery method works cross browser.